reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem
  p in rng f implies (f:-p)/.(len(f:-p)) = f/.len f
proof
A1: len(f:-p) in dom(f:-p) by Th6;
  assume
A2: p in rng f;
  then p..f <= len f by FINSEQ_4:21;
  then reconsider j = len f - p..f as Element of NAT by INT_1:5;
  len(f:-p) = j + 1 by A2,Th50;
  hence (f:-p)/.(len(f:-p)) = f/.(j+p..f) by A2,A1,Th52
    .= f/.len f;
end;
